Report Romance and the Railroad in New Logic/Math Puzzles Posted July 22, 2007 A man has two girlfriends, reachable only by train. One lives to the North, the other to the South. Being a man, he is incapable of deciding which to marry. Since a train leaves his station each hour to the North, and another leaves each hour to the South, he decides to leave his amorous visits to chance. Let Fate decide. Being a clever person, he creates a device that sounds an alarm at a random time of the day. Each day, promptly after the alarm sounds, he takes the 5-minute walk to his station and boards the next train to arrive: Northbound or Southbound. After a year has passed, he finds he has visited one of the girlfriends [turns out it was the one to the South] more than 300 times, and so he marries her. Assuming his random time-of-day device was working properly, how could this have happened? What times did the trains leave the station? The trains to the North left the station on the hour; the trains to the South left at ten minutes after the hour. Each hour there was a 10-minute window for the Northbound train, and a 50-minute window for the Southbound train. After more than 360 days, 300 Southbound trips would be expected.